1. Field of the Invention
The present invention relates generally to magnetic resonance tomography, (MRT) as is used in the field of medicine for the examination of patients. The present invention relates in particular to a method, and to an MRT apparatus for implementing such a method, wherein partial parallel acquisition (PPA) is used for projection reconstructions, i.e., with radial data acquisition.
2. Description of the Prior Art
MRT is based on the physical phenomenon of nuclear spin resonance, and has been used successfully for more than 20 years as an imaging method in medicine and in biophysics. In this examination modality, the subject is exposed to a strong, constant magnetic field. This causes the nuclear spins of the atoms in the subject, which were previously oriented randomly, to become aligned. Radio-frequency energy can now excite these “ordered” nuclear spins to a particular oscillation. This oscillation produces the actual measurement signal in MRT, which is acquired by suitable reception coils. Through the use of non-homogenous magnetic fields, produced by gradient coils, the measurement subject can be spatially coded in all three spatial directions. The method allows a free choice of the volume to be imaged, so tomograms of the human body can be recorded in all directions. As a tomography modality in medical diagnostics, MRT is primarily distinguished, as a non-invasive examination method, by a versatile capacity for contrast. Due to its excellent representation of soft tissue, MRT has developed into a method that is in many ways superior to x-ray computed tomography (CT). Today, MRT is based on the use of spin echo and gradient echo sequences that enable excellent image quality with measurement times on the order of magnitude of minutes.
Constant further technological development of the components of MRT devices, and the introduction of rapid imaging sequences, has continued to open new areas of use for MRT in the field of medicine. Real-time imaging for the support of minimally invasive surgery, functional imaging in neurology, and perfusion measurement in cardiology are only a few examples. Despite the technical progress in the design of MRT devices, the exposure time for an MRT image remains the limiting factor for many MRT applications in the area of medical diagnostics. A limit is placed on any further increase in the efficiency of MRT devices with respect to the exposure time from the technical point of view (feasibility) and for the protection of the patient (stimulation and heating of tissue). In recent years, many efforts have therefore been made to find new approaches to further reduce the image measurement time.
One approach to shortening the acquisition time is to reduce the number of measurement steps. In order to obtain a complete image from such a data set, either the missing data must be reconstructed using suitable algorithms or the erroneous image must be corrected from the reduced data.
Data acquisition in MRT takes place in k-space (frequency domain). The MRT image in the image domain is linked to the MRT data in k-space by means of Fourier transformation. The spatial coding of the subject, which spans k-space, can take place in various ways; however, the most common is a Cartesian scanning or a scanning by projections. The coding takes place by means of gradients in all three spatial directions. In Cartesian scanning, a distinction is made between slice selection (defines an exposure slice in the subject, e.g. the z-axis), frequency coding (defines a direction in the slice, e.g. the x-axis), and phase coding (determines the second dimension inside the slice, e.g. the y-axis).
In an acquisition method for projection reconstruction, a gradient is used that is not successively increased for scanning line-by-line in the Cartesian format, but instead is rotated around the sample. In this way, in each measurement step a projection is obtained from a particular direction through the entire sample, and thus a typical data set is obtained for the projection reconstruction in the k-space, as is shown in FIG. 3. The totality of the points, corresponding to the acquired data in k-space, is hereinafter referred to as the projection data set.
In contrast to Cartesian scanning, radial (or spiral) scanning of the frequency domain is advantageous particularly in the imaging of moving objects such as a beating heart, because motion artifacts in the image reconstruction are smeared over the entire image field, and thus are not noticeable. In contrast, in Cartesian scanning of the frequency domain, in the reconstructed image phantom images occur that are usually disturbing and that are expressed as image structures that repeat periodically in the phase coding direction. However, a disadvantage of radial scanning of the frequency domain is the longer measurement time required in comparison with Cartesian scanning for a nominally equal spatial resolution. In Cartesian scanning, the number of phase coding steps Ny determines the measurement time, while in radial scanning this is determined by the number of angular steps Nφ. For identical spatial resolution, Nφ=(π/2) Ny.
Most methods for shortening the image measurement time in Cartesian scanning are based on a reduction of the plurality of time-consuming phase coding steps Ny and the use of a plurality of signal reception coils; called partial parallel acquisition, or PPA. This principle can be carried over to data acquisition methods using radial scanning, by reducing the number of time-consuming angular steps Nφ.
The basis for PPA imaging is that the k-space data are acquired not by an individual coil, but rather by component coils disposed around the subject in linear, annular, or matrix-type fashion, for example in the form of a coil array. As a result of their geometry, each of the spatially independent components of the coil array supplies certain spatial information that is used to achieve a complete spatial coding by combining the simultaneously acquired coil data. This means that for radial k-space scanning, a number of “omitted” projections in k-space can be determined from a single acquired k-space projection.
Thus, PPA methods use spatial information contained in the components of a coil array in order to partially replace the time-consuming additional switching of the rotating gradients. In this way, the image measurement time is reduced corresponding to the ratio of the number of projections of the reduced projection data set to the number of lines of the conventional (i.e. complete) data set. In a typical PPA acquisition, in comparison to conventional acquisition, only a fraction (one-half, one-third, one-fourth, etc.) of the projections are acquired. A specific reconstruction is then applied to the projection data in order to reconstruct the missing projections, and thus to obtain the complete field of view (FOV) image in a fraction of the time. The FOV is defined by the size of k-space under consideration, according to the factor 2π/k.
A method for using parallel data acquisition with radial scanning of the frequency space is described, for example, in U.S. Pat. No. 6,710,686, by reconstructing partial images for each coil from a reduced number of projections that are superposed in a locally precise manner.
This known method is based on the Fourier shift theorem, which assigns, to a shift of a point having polar coordinates k, φ in the frequency space by the vector Δ k a multiplication of the core magnetization in the spatial domain with the harmonic elΘ, the phase being given by Θ=Δ k r. In the case of magnetic resonance tomography, k means the time sum of the magnetic field gradients applied to the examination subject during the reading out of the nuclear resonance signal. Additional coordinates, quantities, and abbreviations used in the following are illustrated on the basis of FIG. 2:
x, y: Cartesian locus coordinates
r, α: polar locus coordinates
  r  =                    x        2            +              y        2            tga=y/x;k=∫Gdtφ: time sum of the readout gradientφ: direction of the readout gradientΔΦ=φi+1−φi ψ=φ−α
Established PPA methods for Cartesian data acquisition, such as SMASH or GRAPPA, already make use of the Fourier shift theorem, by impressing an additional phase Δky y onto the magnetic resonance signal along the phase coding direction through combination of the individual coil signals. In this way, new ky lines arise in the frequency domain that no longer need be measured explicitly, thus reducing the measurement time.
For radial scanning of the frequency domain, the frequency domain must be occupied with radii having length K=π/ΔR, rotated by the angular step ΔΦ=φi+1−φl=π/KR, so that sufficient data are present for a complete image reconstruction. ΔR represents the locus resolution desired in the image; R is the radius of the desired image field. However, if M signal recording coils are available, in the known method up to M−1 additional angular intermediate steps Δφn (n=1, 2, . . . M−1) can be generated without measurement, so that the angular step to be measured can be increased to the value
      ΔΦ    =          M      ⁢                          ⁢              π        KR              ,and the measurement time can be correspondingly reduced.
For the individual coil m (1<m≦M), the coil signal in polar coordinates is given by
                                                                                          F                  m                                ⁡                                  (                                      k                    ,                    φ                                    )                                            =                            ⁢                                                ∫                                      -                    Y                                    Y                                ⁢                                                      ∫                                          -                      X                                        X                                    ⁢                                                                                    S                        m                                            ⁡                                              (                                                  x                          ,                          y                                                )                                                              ⁢                                          M                      ⁡                                              (                                                  x                          ,                          y                                                )                                                              ⁢                                          ⅇ                                              ⅈ                        ⁢                                                                                                  ⁢                        kr                        ⁢                                                                                                  ⁢                        cos                        ⁢                                                                                                  ⁢                        φcos                        ⁢                                                                                                  ⁢                        α                                                              ⁢                                          ⅇ                                              ⅈ                        ⁢                                                                                                  ⁢                        kr                        ⁢                                                                                                  ⁢                        sin                        ⁢                                                                                                  ⁢                        φ                        ⁢                                                                                                  ⁢                        sin                        ⁢                                                                                                  ⁢                        α                                                              ⁢                                                                                  ⁢                                          ⅆ                      x                                        ⁢                                                                                  ⁢                                          ⅆ                      y                                                                                                                                              =                            ⁢                                                ∫                  0                  π                                ⁢                                                      ∫                                          -                      R                                        R                                    ⁢                                                                                    S                        m                                            ⁡                                              (                                                  r                          ,                          α                                                )                                                              ⁢                                          M                      ⁡                                              (                                                  r                          ,                          α                                                )                                                              ⁢                                          ⅇ                                              ⅈ                        ⁢                                                                                                  ⁢                        kr                        ⁢                                                                                                  ⁢                                                  cos                          ⁡                                                      (                                                          φ                              -                              α                                                        )                                                                                                                ⁢                    r                    ⁢                                                                                  ⁢                                          ⅆ                      r                                        ⁢                                                                                  ⁢                                          ⅆ                      α                                                                                                                                                            ⁢                                                1                  <                  m                  ≤                  M                                ,                                                                        (        1        )            Sm(x, y): sensitivity profile of coil m in Cartesian coordinatesSm(r, a): sensitivity profile of coil m in polar coordinatesM (x, y): cross-magnetization
The overall magnetization at the point k, φ in the frequency space results as the superposition of the individual coil values.
                                          G            O                    ⁡                      (                          k              ,              φ                        )                          =                              ∑                          m              =              1                        M                    ⁢                                    F              M                        ⁡                          (                              k                ,                φ                            )                                                          (                  2          ⁢          a                )            
If weighted sum profiles are now produced from the sensitivity profiles of the coils such that there arise harmonics
                                                        ∑                              m                =                1                            M                        ⁢                                          C                nm                            ⁢                                                S                  m                                ⁡                                  (                                      r                    ,                    α                                    )                                                              ≈                      ⅇ                          ⅈΘ              n                                      ,                  0          ≤          n          ≤                      M            -            1                                              (        3        )            having the argumentΘn=kr(cos(ψ−nΔφ)−cos ψ),  (4a)which for nΔφ<<1 reduces toΘn=kr sin ΨnΔφ,  (4b)then from the coil signals up to M−1, new magnetizations can be calculated in the frequency space at the points k, φ+nΔφ.
                                                                                          G                  n                                ⁡                                  (                                      k                    ,                                          φ                      +                                              n                        ⁢                                                                                                  ⁢                        Δφ                                                                              )                                            =                            ⁢                                                F                  m                                ⁡                                  (                                      k                    ,                    φ                                    )                                                                                                        =                            ⁢                                                ∑                                      m                    =                    1                                    M                                ⁢                                                      C                    nm                                    ⁢                                                            ∫                      0                      π                                        ⁢                                                                  ∫                                                  -                          R                                                R                                            ⁢                                                                                                    S                            m                                                    ⁡                                                      (                                                          r                              ,                              α                                                        )                                                                          ⁢                                                  M                          ⁡                                                      (                                                          r                              ,                              α                                                        )                                                                                                                                                                                                                                    ⁢                                                ⅇ                                      ⅈ                    ⁢                                                                                  ⁢                    kr                    ⁢                                                                                  ⁢                                          cos                      ⁡                                              (                                                  φ                          -                          α                                                )                                                                                            ⁢                r                ⁢                                                                  ⁢                                  ⅆ                  r                                ⁢                                                                  ⁢                                  ⅆ                  α                                                                                                        =                            ⁢                                                ∫                  0                  π                                ⁢                                                      ∫                                          -                      R                                        R                                    ⁢                                                            ⅇ                                              ⅈΘ                        n                                                              ⁢                                          M                      ⁡                                              (                                                  r                          ,                          α                                                )                                                              ⁢                                          ⅇ                                              ⅈ                        ⁢                                                                                                  ⁢                        kr                        ⁢                                                                                                  ⁢                                                  cos                          ⁡                                                      (                                                          φ                              -                              α                                                        )                                                                                                                ⁢                    r                    ⁢                                                                                  ⁢                                          ⅆ                      r                                        ⁢                                                                                  ⁢                                          ⅆ                      α                                                                                                                                              =                            ⁢                                                ∫                  0                  π                                ⁢                                                      ∫                                          -                      R                                        R                                    ⁢                                                            M                      ⁡                                              (                                                  r                          ,                          α                                                )                                                              ⁢                                          ⅇ                                              ⅈ                        ⁢                                                                                                  ⁢                        kr                        ⁢                                                                                                  ⁢                                                  cos                          ⁡                                                      (                                                          φ                              +                                                              n                                ⁢                                                                                                                                  ⁢                                Δφ                                                            -                              α                                                        )                                                                                                                ⁢                    r                    ⁢                                                                                  ⁢                                          ⅆ                      r                                        ⁢                                                                                  ⁢                                          ⅆ                      α                                                                                                                              (        5        )            
The newly calculated points result from the shifting of a respective measured point in the frequency space (FIG. 2).
A disadvantage of this method is that in order to be able to indicate this coefficient C, the precise knowledge of the coil profile Sm is required. Conventionally, this has been explicitly obtained with additional measurement steps, and, generally using a calibration measurement carried out before the actual imaging or integrated into the actual measurement sequence, requiring a significant additional measurement expense.